2 Find formula for the frequency of the small radial oscillations of the... · OlympiadBench #1099
Physics · thermodynamics
Problem
2 Find formula for the frequency ω of the small radial oscillations of the bubble and evaluate it under the assumption that the heat capacity of the soap film is much greater than the heat capacity of the gas in the bubble. Assume that the thermal equilibrium inside the bubble is reached much faster than the period of oscillations.
Hint: Laplace showed that there is pressure difference between inside and outside of a curved surface, caused by surface tension of the interface between liquid and gas, so that Δp=r2σ.
Given constants:
A bubble of radius r=5.00cm, containing a diatomic ideal gas, has the soap film of thickness h=10.0μm and is placed in vacuum. The soap film has the surface tension σ=4.00⋅10−2mN and the density $\rho=1.10 \frac{\mathrm{g}}{\mathrm{cm}^{3}} .
Context question:
1 Find formula for the molar heat capacity of the gas in the bubble for such a process when the gas is heated so slowly that the bubble remains in a mechanical equilibrium and evaluate it;
Hint: Laplace showed that there is pressure difference between inside and outside of a curved surface, caused by surface tension of the interface between liquid and gas, so that Δp=r2σ.
Context answer:
33.2